Multiply the numerator & denominator by 1/n .mmilton said:Homework Statement
Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit?
Homework Equations
The Attempt at a Solution
I believe it does converge because the higher power is in the denominator, so thus, it's limit is 0.
Any help or hints on if I'm headed in the right direction would be very much appreciated!
Thank you in advance.
Convergence in mathematics refers to the behavior of a sequence or series as its terms approach a specific value or limit. In other words, as the number of terms increases, the values of the terms get closer and closer to a particular value.
Yes, the sequence {n/(n^2+1)} is convergent. It converges to the value 0 as n approaches infinity.
There are various methods for proving the convergence of a sequence or series, including the comparison test, the ratio test, and the root test. These tests involve analyzing the behavior of the terms or the ratio of consecutive terms in the sequence or series.
Determining if a sequence or series is convergent is important in many areas of mathematics, such as calculus and real analysis. It allows us to make accurate predictions and calculations, and it is essential for understanding the behavior and properties of functions and equations.
No, a sequence or series cannot be both convergent and divergent. It can only have one of these properties. If the terms of a sequence or series approach a single value, it is convergent. If the terms do not approach a single value, it is divergent.